Kripke Incompleteness of Some Predicate Extensions of Modal Subframe Logics without Finite Embedding Property
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چکیده
Let Q-L be the least predicate extension of a normal extension L of S4 and BF be the Barcan formula ∀x2A(x) ⊃ 2∀xA(x). Ghilardi [3] showed that it is rare that Q-L is complete with respect to Kripke semantics. On the other hand, if L is a subframe logic with the finite embedding property, we can show the completeness of Q-L + BF by the method of canonical models (cf. Lemma 3 [2], Theorem 3.9 [5]). It is natural to ask whether Q-L+BF is complete if L is a subframe logic without finite embedding property. Cresswell [4, chapter 14] described a proof due to Fine of the incompleteness of Q-S4M = Q-S4 + 23p ⊃ 32p + BF and asked whether Q-S4.3.1+ BF is complete or not (
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تاریخ انتشار 2007